Seismic surface-related multiples have become a hot topic of great significance due to the buried geological information provided by broader illumination areas than primaries. In recent years, researchers attempt to extract the hidden hint of multiples rather than treating them as noise and eliminating them directly. The elimination methods, e.g., the surface-related multiple elimination (SRME) and the inverse scattering series free-surface multiple elimination (ISS-FSME), may be affected by the overlapping or proximity of primaries and multiples. Typical imaging methods, e.g., the reverse time migration (RTM) and the least-square reverse time migration (LSRTM), suffer severe crosstalk artifacts from multiples of inappropriate order and smooth migration velocities. To study the characteristics of primaries and surface-related multiples, whether for elimination or imaging, we propose a forward modeling method of acoustic surface-related order-separated multiples established on the areal/virtual source assumption. The free surface is replaced with an absorbing surface under the dipole source approximation and the ghost creation approach. We present two reflection operators to approximate the reflection at the free surface and apply them to the areal source to obtain ideal results. Numerical experiments on three models prove the effectiveness of the proposed forward modeling method of acoustic surface-related order-separated multiples.

由于比一次地震更广泛的照明区域提供了埋藏的地质信息，与地震表面相关的多次波已成为具有重要意义的热门话题。近年来，研究人员试图提取倍数的隐藏暗示，而不是将它们视为噪音并直接消除它们。消除方法，例如表面相关多重消除(SRME)和逆散射系列自由表面多重消除(ISS-FSME)，可能会受到一次和多次的重叠或接近的影响。典型的成像方法，例如逆时偏移（RTM）和最小二乘逆时偏移（LSRTM），由于不适当的阶次和平滑偏移速度的倍数而遭受严重的串扰伪影。为了研究一次波和表面相关多次波的特征，无论是用于消除还是成像，我们提出了一种基于面/虚拟源假设建立的声学表面相关阶次分离多次波的正演建模方法。在偶极源近似和重影创建方法下，自由表面被吸收表面取代。我们提出了两个反射算子来近似自由表面的反射，并将它们应用于面源以获得理想的结果。三个模型的数值实验证明了所提出的声表面相关阶次多次波正演建模方法的有效性。